Youth hunting rifle...
Last minute thought 243. IS cheaper to shoot with a better variety of bullets.
Some of the younger hunters in our group used 7mm-08 youth rifles and have had excellent results with it. The only time we had to track a deer was when the young hunter gut shot one. We recovered that one too.
Some of the young hunters are staying with 7mm-08s even when they outgrow the youth rifles.
I hope your son has a lot of fun killing deer with the 7mm-08.
It offer a large selection of .284 caliber bullets and is a relatively easy shooting rifle.
Nothing wrong with the .243, and without starting any arguments its a marginal caliber that requires solid bullet placement.
Go with the 7mm-08 and don't look back in IMHO.
Shoot straight and shoot often GF